\section{Conclusion}

If ever one is in need of calculating something of reasonable size,
and no party wants to trust a central authority with their private
input data, then this system is a very viable option for doing that. I
have in this thesis shown it is indeed possible in practice, and is not
just a theoretical possibility. I have shown that the bounds on the
communication complexity are probable, but have not been able to
conclude anything for large circuits. One of the real life problems is
making sure only $t$ players are corrupted. This need not be a
problem, however, since it depends on the setting of the problem we
want to solve. If for instance the problem concerns privacy more than
security of getting the correct output, then you might trust that
enough parties just wants to know the output rather than tweak the
results. One must remember that the system is not only secure against
false messages, but also keeps your input data safe and private. In a
normal auction case most people worry about others not knowing their
bid, and does not really think of making the system fail. Naturally it
is possible, but it would require a huge effort from the adversary who
has to control all $t$ corrupt parties. If some of them just sends bad
info, but does not cooperate with the adversary, they will not help
gaining the adversary information, only making the protocol fail. This
is the same as saying that we still obtain privacy, but there is no
correctness. Also, think of a vote for democracy in a dictatorship. If
we look past the practical complications of having such a gigantic
system in place, to alter the outcome of this you would need to have
$\nicefrac{n}{3}$ of the population on your side, and if that happens
I guess there is no need to cheat the system in the first place. The
point is that is it indeed viable to install for real life scenarios
if one could get past the practical problems of doing so. Of course
the practical problems in a national election are pretty huge, as
every citizen needs to obtain a secure computer and everyone has to be
online at the same time or else the election would take a very long
time. Also, the communication overhead is $O(n^3)$, which is not
linear in the number of players, thus you would like to keep $n$ to a
minimum such that the overhead does not exceed the cost of the
multiplication gates. Thus, if this system is used for voting in real
life, it should be kept to a small scale with few players, but then it
has potential to be a success.
